A213223 a(n) = 10^n + 10*n.

1, 20, 120, 1030, 10040, 100050, 1000060, 10000070, 100000080, 1000000090, 10000000100, 100000000110, 1000000000120, 10000000000130, 100000000000140, 1000000000000150, 10000000000000160, 100000000000000170, 1000000000000000180, 10000000000000000190, 100000000000000000200

Offset: 0

Author

Vincenzo Librandi, Mar 03 2013

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-21,10).

Crossrefs

Cf. A198400.

Programs

Magma

[10^n + 10*n: n in [0..25]];

Magma

I:=[1, 20, 120]; [n le 3 select I[n] else 12*Self(n-1)-21*Self(n-2)+10*Self(n-3): n in [1..30]];

Mathematica

Table[(10^n + 10 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 8 x - 99 x^2)/((1 - x)^2 (1 - 10 x)), {x, 0, 30}], x]

Formula

G.f.: (1+8*x-99*x^2)/((1-x)^2*(1-10*x)).

a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n > 2.

E.g.f.: exp(x)*(exp(9*x) + 10*x). - Elmo R. Oliveira, Aug 29 2024